1. Field of the Invention
The invention concerns the reconstruction of a two-dimensional (2D) or three-dimensional (3D) image of an object, for example part of a region of interest in a patient, on the basis of a set of one-dimensional or two-dimensional views respectively of the region of interest, taken from different positions by an imaging system around the region of interest. The invention finds particular application in medical imaging by tomography reconstruction or Few-View Tomography.
2. Description of the Prior Art
With tomography it is possible to produce slice images of a region of interest of an object, by acquiring projections.
FIG. 1 schematically illustrates the acquisition of 2D images of a body organ and the reconstruction of this organ as a 3D image by tomosynthesis.
X-rays R derived from a source S are emitted at different angles (1, . . . , i, . . . , n) towards the organ O. After passing through the organ they are detected by the detector Dct forming a set of 2D projections, s1, . . . , si, . . . , sn. It is to be noted that there are as many acquired 2D projections as there are angles under consideration. If all the angles cover at least a semicircle, the term tomography is used. When this condition cannot be met (for example: arc of a circle of less than 180 degrees, straight line) the term tomosynthesis is used.
Acquisition is obtained using a detector positioned facing an X-ray source, e.g. a digital camera.
One application of tomography is the detection and characterization of a lesion in an organ, e.g. a cancer lesion. For the breast, tomosynthesis is used.
The acquired 2D projections are used to reconstruct a 3D image of the object. This 3D image is more precisely a 3D map of the X-ray attenuation coefficients of the medium through which the rays have passed.
It is this mapping that is used by a radiologist to interpret this image in relation to the observed differences in contrast.
3D reconstruction of the image is a costly, complex operation, in particular if it uses an iterative algorithm.
An iterative 3D reconstruction method is known. This method is based on a discrete, matrix expression of the topographic reconstruction problem.
More precisely the problem can be modelled by the following equation:Rf=s in which s is a vector of the acquired projections, R is a projection operator which models the topographic imaging system and f is the 3D image of the object to be reconstructed.
The problem to be solved with tomographic reconstruction is to determine f having knowledge of s and R.
Exact reconstruction of the 3D image f in theory requires a set of measurements at least as large as the number of unknowns forming the 3D image, measured under the constraints of tomography i.e. measurements with a very small sampling pitch and a rotation of 180 degrees about the object.
In practice, this may prove to be impossible for the following reasons:
Firstly, in examinations of tomosynthesis type, it is not possible to obtain measurements at 180° around the object to be imaged, and secondly the smaller the sampling pitch the higher the number of measurements, which increases the duration of examinations and hence the applied X-ray dose.
Therefore the case is frequently encountered in tomography in which the size of the 3D image is much larger than the size of the data, which implies solving a system having a very high number of possible solutions.
The choice of reconstruction method allows a 3D image to be found that is an acceptable solution for the intended application.
Additionally, known space reconstruction methods of 3 images are in the form of an iterative algorithm defined by its iteration A which generates a reconstruction f(n) of the solution from a reconstruction f(n-1) such that:f(n)=A[f(n-1)].
Starting with an initial reconstruction denoted f(0) in the series of reconstructions f(n), the reconstruction at iteration N is obtained as:
      f          (      N      )        =            A      ⁡              [                  f                      (                          N              -              1                        )                          ]              =                  A        ⁡                  [                      A            ⁡                          [                              f                                  (                                      N                    -                    2                                    )                                            ]                                ]                    =                                    A            2                    ⁡                      [                          f                              (                                  N                  -                  2                                )                                      ]                          =                  …          =                                                    A                i                            ⁡                              [                                  f                                      (                                          N                      -                      i                                        )                                                  ]                                      =                          …              =                                                                    A                    N                                    ⁡                                      [                                          f                                              (                        0                        )                                                              ]                                                  .                                                        
This algorithm requires the storing of initialization steps, of intermediate reconstructions and archiving of the reconstruction, i.e. one or more 3D images depending on whether storing is made simultaneously or successively, and represents a generated amount of data that is much greater than the amount of acquired data (low number of projections).
Some known methods use discrete, matrix (hence linear) operations. Some are associated with solving the linear system Rf=s, others are associated with minimization of the quadratic error ∥Rf−s∥2 sir and of the associated system R′Rf=R′s in which R′ is the transposed matrix of R, others generalize the preceding approach by solving a system RRf= Rs in which R is a matrix such that RRf is a 3D image. Reference can be made to the document <<CIARLET, P. G., Introduction á l'Analyse Numerique MairieieIle el á l'Optinnsation, Masson. Paris, 1982>>.
More recently, it was proposed to calculate a filter iteratively, and once and for all, the filter being obtained by iterative reconstruction of a test object and to apply this filter to every object to be imaged at the acquired projections in order to obtain the reconstructed volume of the object without any iterative computing. In this respect, reference can be made to document U.S. Pat. No. 7,447,295. In this way, the required computing power is reduced compared with iterative methods. However, the substitution of iterative reconstruction by filtering generates loss of data. It is therefore a near-approach method.